∫2x+5√(3x+2)dx ..... (1) Let 3x+2=t^2 ⇒ 3 dx 2t dt ⇒ dx=23t dt eqn (1) becomes ∫2.(t^2 2)5=23t dtt =2^23^2∫ (t^2 2)dt =4 ...

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Property 1

Solve ∫2x +...

Question

Solve $\int \frac{2 x + 5}{\sqrt{3 x + 2}} d x$

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Solution

$\int \frac{2 x + 5}{\sqrt{3 x + 2}} d x . . . . . (1)$
Let $3 x + 2 = t^{2}$
$\Rightarrow 3 d x - 2 t d t$
$\Rightarrow d x = \frac{2}{3} t d t$
eqn $(1)$ becomes
$\int \frac{2. \frac{(t^{2} - 2)}{5} = \frac{2}{3} t d t}{t}$
$= \frac{2^{2}}{3^{2}} \int (t^{2} - 2) d t$
$= \frac{4}{9} (\frac{t^{3}}{3} - 2 t + C)$
$= \frac{4}{9} (\frac{\sqrt{3 x + 2}}{5} - 2 \sqrt{3 x + 2} + C)$

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